In this paper, the concept of contraction mapping on a -metric space is extended with a consideration on local contraction.  As a result, two fixed point theorems were proved for contraction on a closed ball in a complete -metric space.

In this research, a new application has been developed for games by using the generalization of the separation axioms in topology, in particular regular, Sg-regular and SSg- regular spaces. The games under study consist of two players and the victory of the second player depends on the strategy and choice of the first player. Many regularity, Sg, SSg regularity theorems have been proven using this type of game, and many results and illustrative examples have been presented

This paper is concerned with introducing and studying the o-space by using out degree system (resp. i-space by using in degree system) which are the core concept in this paper. In addition, the m-lower approximations, the m-upper approximations and ospace and i-space. Furthermore, we introduce near supraopen (near supraclosed) d. g.'s. Finally, the supra-lower approximation, supraupper approximation, supra-accuracy are defined and some of its properties are investigated.

This study aimed to investigate the incorporation of recycled waste compact discs (WCDs) powder in concrete mixes to replace the fine aggregate by 5%, 10%, 15% and 20%. Compared to the reference concrete mix, results revealed that using WCDs powder in concrete mixes improved the workability and the dry density. The results demonstrated that the compressive, flexural, and split tensile strengths values for the WCDs-modified concrete mixes showed tendency to increase above the reference mix. However, at 28 days curing age, the strengths values for WCDs-modified concrete mixes were comparable to those for the reference mix. The leaching test revealed that none of the WCDs constituents was detected in the leachant after 180 days. The

 In this paper, two elements of the multi-input multi-output (MIMO) antenna had been used to study the five (3.1-3.55GHz and 3.7-4.2GHz), (3.4-4.7 GHz), (3.4-3.8GHz) and (3.6-4.2GHz) 5G bands of smartphone applications that is to be introduced to the respective US, Korea, (Europe and China) and Japan markets. With a proposed dimension of 26 × 46 × 0.8 mm³, the medium-structured and small-sized MIMO antenna was not only found to have demonstrated a high degree of isolation and efficiency, it had also exhibited a lower level of envelope correlation coefficient and return loss, which are well-suited for the 5G bands application. From the fabrication of an inexpensive FR4 substrate with a 0.8 mm thickness level, a loss tang

A complete metric space is a well-known concept. Kreyszig shows that every non-complete metric space  can be developed into a complete metric space , referred to as completion of .

We use the b-Cauchy sequence to form  which “is the set of all b-Cauchy sequences equivalence classes”. After that, we prove  to be a 2-normed space. Then, we construct an isometric by defining the function from  to ; thus  and  are isometric, where  is the subset of  composed of the equivalence classes that contains constant b-Cauchy sequences. Finally, we prove that  is dense in ,  is complete and the uniqueness of  is up to isometrics

The aim of this paper is to study the best approximation of unbounded functions in the
weighted spaces
,
1, 0 ,
p
p L α
α ≥>.
Key Words: Weighted space, unbounded functions, monotone approximation

The objective of this paper is to define and introduce a new type of nano semi-open set which called nano -open set as a strong form of nano semi-open set which is related to nano closed sets in nano topological spaces. In this paper, we find all forms of the family of nano -open sets in term of upper and lower approximations of sets and we can easily find nano -open sets and they are a gate to more study.  Several types of nano open sets are known, so we study relationship between the nano -open sets with the other known types of nano open sets in nano topological spaces. The Operators such as nano -interior and nano -closure are the part of this paper.

The pharmacy is the face for the health buildings and hospitals, The linking professional relationships and functional, it is been from the important places that most people go it, so according to that we must format its interior design in form that suitable with the need of most people use it or work in it, and this the search goal, dashing from the search subject which to hide finding designer treatment for the pharmacies interior spaces, to give share in the functional improvement performance or aesthetic. We define the search goals to share in educate the pharmacist in the effect of interior design for improvement of interior environment, in addition to the search consider as designer trying add to the other trying the interior desig